chaos theory discusses unstable and non-periodic behavior of non-linear fluctuating dynamicsystems. since evaporation level variations of lakes have a dynamic identity, chaos theory can have a uniquerole in collecting data of these variations. therefore it is an important and challenging problem in the field ofplanning and qualitative and quantitative management of urmia lake to verify whether ...

Abstract: The dynamics of network traffic are complex and nonlinear, and chaotic behaviors and their prediction, which play an important role in local area networks (LANs), are studied in detail, using the largest Lyapunov exponent. With the introduction of phase space reconstruction based on the time sequence, the high-dimensional traffic is projected onto the low dimension reconstructed phase...

We present a fast, simple matrix method of computing the unique invariant measure and associated Lyapunov exponents of a nonlinear iterated function system. Analytic bounds for the error in our approximate invariant measure (in terms of the Hutchinson metric) are provided, while convergence of the Lyapunov exponent estimates to the true value is assured. As a special case, we are able to rigoro...

The commutator $[x(t),p]$ in an inverted harmonic oscillator (IHO) one-dimensional quantum mechanics exhibits remarkable properties. It reduces to a c-number and does not show any fluctuations for arbitrary states. Related this nature, the Lyapunov exponent computed through out-of-time-order correlator (OTOC) $⟨[x(t),p{]}^{2}⟩$ precisely agrees with classical one. Hence, OTOC may be regarded as...